History, motivation, and general considerations

With the first release of ADF in 2002, the existing basis sets have been modified, but also new basis sets have been added. The reason for this is that we would like to facilitate calculations near the basis set limit, allowing users to remove this source of errors from their calculations (at the expense of CPU time). Two circumstances triggered our effort to test and improve the ADF basis sets. The first was the sabbatical of Prof. Del Chong (University of British Columbia, Vancouver, Canada) that he spent in the Theoretical Chemistry group in Amsterdam in the spring of 2000. Professor Chong, who has been involved in the development of basis sets for many years, pointed out to us the power and flexibility of even-tempered (ET) basis sets. These basis sets consist only of 1s, 2p, 3d, etc. functions, of which the factor between neighboring exponents for a certain l-value is a constant. Subsequently he started to develop such Slater Type Orbital (STO) basis sets for use in the ADF program. In the meantime the choice of polarization functions in ADF was reconsidered. The combination of these ET basis sets with improved polarization functions yielded good results in test calculations on molecular binding energies.

Another important factor was the ZORA quadruple zeta (QZ4P) basis developed by Dr. E. van Lenthe. These basis sets had been devised in a similar way as had been done earlier for basis sets I-V in ADF, by fitting each numerical orbital in an atom to several STOs. (Names of these standard basis sets I-V have changed to more intuitive names: I→SZ, II→DZ, III→DZP, IV→TZP, and V→TZ2P. Additionally a large number of polarization functions were added. These basis sets were intended for near basis set limit calculations on small systems. Subsequent tests were performed on many small molecules, in which the quality of various basis and fit sets was compared. The major overall conclusion was that, for normal properties like binding energies, both large ET basis sets and the QZ4P basis sets gave results very close to each other and very close to results obtained in the literature with very large GTO basis sets. This was a pleasing conclusion as we could then use these basis and fit sets to test the old ADF basis and fit sets. Many of such tests were performed by Dr. E. van Lenthe. In these tests occasional deficiencies in the old ADF basis sets were uncovered. Although no strict definition of deficiency was used, a basis set was considered suspect if it led to errors in the bond energy much larger than typical for that size of basis. In such a case the old, suspect basis set was adapted. Such an adaptation usually implied a slightly larger number of functions, or a more logical choice for the number of polarization functions or the exponent of the polarization functions. The changes that were made will be described more fully below.

Prof. Del Chong has devised two improved large basis sets for ADF that become available with ADF2002.03. The TZ2P+ basis set is available for the transition metals Sc-Zn only (Z=21-30). These basis sets are nearly identical to TZ2P except for a better description of the d-space (4 d-functions instead of 3). An improved even-tempered (ET) basis set has also been devised by Del Chong. It is named ET-pVQZ and available for the elements H-Kr. Because of smaller basis set superposition errors, the Et-pVQZ basis is to be preferred over the current ET-QZ3P and ET-QZ+5P basis sets. See also: D.P. Chong, E. Lenthe, S.J.A. van Gisbergen, E.J. Baerends, Even-tempered Slater-Type orbitals revisited: From Hydrogen to Krypton, J. Comp. Chem. 25 (2004) 1030-1036.

In the ADF2005.01 version the TZ2P+ basis set is now available also for the lanthanides (Z=57-70), although only in the ZORA directory. These basis sets are nearly identical to ZORA/TZ2P except for a better description of the f-space (4 f-functions instead of 3).

In the ADF2005.01 version augmented basis sets are available, for use in time-dependent density functional calculations. These are augmented SZ, DZ, DZP, TZP, TZ2P non-relativistic basis sets for H-Kr. They are named ASZ, ADZ, ADZP, ATZP, and ATZ2P, respectively. They are devised by Prof. Del Chong for use in TDDFT calculations, especially for the reasonable accurate calculation of excitation energies, with a relatively small basis set.

In the ADF2006.01 version non-relativistic all electron basis sets optimized for Hartree-Fock calculations are available in the subdirectory Special/Bunge. Ref. C.F.Bunge, J.A.Barrientos and A.V.Bunge, Atomic Data and Nuclear Data Tables 53,113-162(1993). Only to be used in atomic calculations, since polarization functions are missing.

Further details are given in the README files in the basis set directories.